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Appendix   VI.

1201

reference plane, which has been taken at centre of crank I. The
force polygon is next constructed of the three forces, i, 1-52, i,
and the closing line will shew the required direction of crank I,
as well as the value of the mass ("565) to be placed on the crank.
It must, however, be remembered, from our first conditions, that
§ of this mass must reciprocate, while |- revolves.

Engines of accurately-balanced design have already been shewn
at A and c, p. 898, and at Fig. 1057, while the method of approxi-
mate balance adopted in locomotives is also described at p. 898,
where the only matter of doubt is the proportion of reciprocating
weights that are to be treated as revolving. This proportion,
formerly commencing at -| to \ in the older and lighter engines,
has now been increased to |- or £ in the heavier modern
locomotives, f being the average fraction; D and E, Fig. 10570,
are further balanced examples.

CHAPTER XL

P. 714. Coefficient of Discharge.—Fig. 1058 shews a
laboratory apparatus designed to measure with accuracy the flow
of water over notches, either for proving the law or for deter-
mining the Coefficient of Discharge. The apparatus will be here
described as arranged for ascertaining the coefficient of a rec-
tangular notch at various heads. Water flows through a i in.
pipe into the tipper tank A, being steadied by the perforated
plates at D, and, flowing quietly over the notch H, arrives in the
larger or measuring tank B, from which it can be drained at K.
The notch plate is shewn at (6), being if" wide and nearly knife-
edged. At (2) a weight Gx carries a needle that is adjusted
vertically downwards from a bracket at front of tank A, till its
point is level with the lower edge of the notch. The float EX ,
at (4), rests on the water in tank A and slides vertically on glass
rods ti XT fixed to the bar s. This bar also carries a fine scale R,
to shew the float level by the pointer Q, carried on a wire N.
When needle J (2) has been levelled with the knife-edge, water is
permitted to rise till it just touches the needle, and the float
height is noted. This must be done with very great accuracy, so